#H0:My average daily screen time is less than or equal 2. #Ha:My average daily screen time exceeds the 2 hours recommended time.

#Experts say adults should limit screen time to 2 hours. In this case, i will be using recommended limit time of 2 hours.

\(H0: p = 2.0\) \(Ha:p > 2.0\)

library(tidyverse)
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library(ggplot2)
library(plotly)
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library(readxl)
ScreenTime <- read_excel("/Users/AhmedFarah/Documents/Data Science/ScreenTime.xlsx")
graph1 <- ggplot(ScreenTime, aes(x=Day, y=ScreenTime, color= Day))+geom_line() + geom_point()+ labs(title = "Daily Screen Time Over Two Weeks", x="Day", y="Screen Time (hours)")

ggplotly(graph1)

#Each point on the line shows the screen time for a specific day

#Histogram of screen time disribution

graph2 <- ggplot(ScreenTime, aes(x=ScreenTime))+geom_histogram(binwidth = 0.5, fill="skyblue", color="black")+labs(title = "Distribution of Daily Scrreen Time", x="Screen Time (hours)", y="Frequency")

ggplotly(graph2)

#The histogram shows the disribution of daily screentime, with each bar representing the frequency of screen time within a certain range of hours.

#boxplot

graph3 <- ggplot(ScreenTime, aes(y = ScreenTime)) + geom_boxplot(fill="lightgreen", color="black")+ labs("Boxplot of Daily Screen Time", y="Screen Time (Hours)")

ggplotly(graph3)

#no outliers for the Screen time data. Screen time is between 2.5 - 6.5

One-sample t-test

t.test(ScreenTime$ScreenTime, mu=2, alternative = "greater")
## 
##  One Sample t-test
## 
## data:  ScreenTime$ScreenTime
## t = 6.1287, df = 14, p-value = 1.306e-05
## alternative hypothesis: true mean is greater than 2
## 95 percent confidence interval:
##  3.567748      Inf
## sample estimates:
## mean of x 
##       4.2

We reject the null hypothesis because the average daily screen is signifacnly greater than the 2 hour limit suggested for screen time.

#Two-sample t-test #H0:There is no significant difference between the average screen time on weekends and weekdays.

#HA: The average screen time on weekends differs from weekdays.

\(H0: weekends = weekdays\) \(Ha: weekends \ne weekdays\)

weekdays <- ScreenTime %>% filter(Day %in% c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday"))

weekends <- ScreenTime %>% filter(Day %in% c("Saturday", "Sunday"))

t.test(weekends$ScreenTime, weekdays$ScreenTime, alternative = "two.sided")
## 
##  Welch Two Sample t-test
## 
## data:  weekends$ScreenTime and weekdays$ScreenTime
## t = 2.1958, df = 6.1556, p-value = 0.06937
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1613176  3.1613176
## sample estimates:
## mean of x mean of y 
##       5.3       3.8

#With a p-value = 0.67 we fail to reject the null hypothesis. This proves that there is insuffienct evidence to support that average screen time on weekends differs significantly from weekdays.

#Simple Linear regression

linear <- lm(ScreenTime ~ Day, data=ScreenTime)

summary(linear)
## 
## Call:
## lm(formula = ScreenTime ~ Day, data = ScreenTime)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.25000 -0.22500  0.03333  0.22500  1.25000 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    6.0000     0.4878  12.301 1.77e-06 ***
## DayMonday     -2.5333     0.6297  -4.023  0.00382 ** 
## DaySaturday   -1.6500     0.6898  -2.392  0.04372 *  
## DaySunday      0.2500     0.6898   0.362  0.72643    
## DayThursday   -2.7500     0.6898  -3.987  0.00402 ** 
## DayTuesday    -3.3000     0.6898  -4.784  0.00138 ** 
## DayWednesday  -2.2500     0.6898  -3.262  0.01150 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6898 on 8 degrees of freedom
## Multiple R-squared:  0.8593, Adjusted R-squared:  0.7538 
## F-statistic: 8.145 on 6 and 8 DF,  p-value: 0.00463

#Summary

#The analysis of daily screen time over a two-week period revealed that the mean daily screen time was 4.2 hours, which exceeds the recommended 2-hour limit.

#Hypothesis testing showed that there was no significant difference between the average screen time on weekends and weekdays, indicating consistent screen usage patterns across the week.